Finite Group Databasebeta

← Group #312839

Character table — Group #312839

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-11-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-111-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-11111-1-11-1
χ911111111111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111
χ1011111111111111111-1-1-1-111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-111111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111111-1-1-111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1111-1-1-1-1-1111-1
χ17222222222-22-22-22-2-20000-22222-2-2-2-22200-2-200000000000000000000002-200000000
χ18222222222-22-22-22-2-20000-22222-2-2-2-2-2-200220000000000000000000000-2200000000
χ19222222222-22-22-22-2-20000-2-2-2-2-222222200220000000000000000000000-2-200000000
χ20222222222-22-22-22-2-20000-2-2-2-2-22222-2-200-2-200000000000000000000002200000000
χ2122222222-22-22-22-22-22222-20000000000-2-20022-2-2-2-200002200000000000000000000
χ2222222222-22-22-22-22-22222-20000000000-2-200-2-222220000-2-200000000000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000000000220022-2-2220000-2-200000000000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200000000002200-2-222-2-200002200000000000000000000
χ2522-2-2-22-2222-2-222-2-2-22i2i−2i−2i22i2i−2i−2i2i2i−2i−2i002i−2i0000000022-2-20000000000000000000000
χ2622-2-2-22-2222-2-222-2-2-22i2i−2i−2i2−2i−2i2i2i−2i−2i2i2i002i−2i00000000-2-2220000000000000000000000
χ2722-2-2-22-2222-2-222-2-2-2−2i−2i2i2i22i2i−2i−2i2i2i−2i−2i00−2i2i00000000-2-2220000000000000000000000
χ2822-2-2-22-2222-2-222-2-2-2−2i−2i2i2i2−2i−2i2i2i−2i−2i2i2i00−2i2i0000000022-2-20000000000000000000000
χ2922-2-2-22-222-2-222-2-2220000-22i2i−2i−2i−2i−2i2i2i000000000000000000000000002i−2i002-2000000
χ3022-2-2-22-222-2-222-2-2220000-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000−2i2i00-22000000
χ3122-2-2-22-222-2-222-2-2220000-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000002i−2i00-22000000
χ3222-2-2-22-222-2-222-2-2220000-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000−2i2i002-2000000
χ3322-2-2-22-22-222-2-222-222i2i−2i−2i-20000000000−2i2i0000000000000022-2-22i2i−2i−2i000000000000
χ3422-2-2-22-22-222-2-222-222i2i−2i−2i-20000000000−2i2i00000000000000-2-222−2i−2i2i2i000000000000
χ3522-2-2-22-22-222-2-222-22−2i−2i2i2i-200000000002i−2i0000000000000022-2-2−2i−2i2i2i000000000000
χ3622-2-2-22-22-222-2-222-22−2i−2i2i2i-200000000002i−2i00000000000000-2-2222i2i−2i−2i000000000000
χ372-22-22-2-22020-20-20202i−2i2i−2i0i2−i2i2−i2i2−i2i2−i2000000002-22i−2i2−22−200i2−i2i2−i22−22−2000000000000
χ382-22-22-2-22020-20-20202i−2i2i−2i0i2−i2i2−i2i2−i2i2−i200000000-22−2i2i2−22−200−i2i2−i2i2−22−22000000000000
χ392-22-22-2-22020-20-20202i−2i2i−2i0−i2i2−i2i2−i2i2−i2i2000000002-22i−2i−22−2200−i2i2−i2i2−22−22000000000000
χ402-22-22-2-22020-20-20202i−2i2i−2i0−i2i2−i2i2−i2i2−i2i200000000-22−2i2i−22−2200i2−i2i2−i22−22−2000000000000
χ412-22-22-2-22020-20-2020−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i2000000002-2−2i2i−22−2200i2−i2i2−i2−22−22000000000000
χ422-22-22-2-22020-20-2020−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i200000000-222i−2i−22−2200−i2i2−i2i22−22−2000000000000
χ432-22-22-2-22020-20-2020−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i2000000002-2−2i2i2−22−200−i2i2−i2i22−22−2000000000000
χ442-22-22-2-22020-20-2020−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i200000000-222i−2i2−22−200i2−i2i2−i2−22−22000000000000
χ452-2-22-2-22202020-20-202-2-2202−2−222−2−220000002i−2i00002−2−222i−2ii2−i2−i2i2−i2i2i2−i2000000000000
χ462-2-22-2-22202020-20-202-2-2202−2−222−2−22000000−2i2i00002−2−22−2i2i−i2i2i2−i2i2−i2−i2i2000000000000
χ472-2-22-2-22202020-20-202-2-220−222−2−222−20000002i−2i0000−222−22i−2i−i2i2i2−i2i2−i2−i2i2000000000000
χ482-2-22-2-22202020-20-202-2-220−222−2−222−2000000−2i2i0000−222−2−2i2ii2−i2−i2i2−i2i2i2−i2000000000000
χ492-2-22-2-22202020-20-20-222-202−2−222−2−220000002i−2i0000−222−2−2i2ii2−i2−i2i2i2−i2−i2i2000000000000
χ502-2-22-2-22202020-20-20-222-202−2−222−2−22000000−2i2i0000−222−22i−2i−i2i2i2−i2−i2i2i2−i2000000000000
χ512-2-22-2-22202020-20-20-222-20−222−2−222−20000002i−2i00002−2−22−2i2i−i2i2i2−i2−i2i2i2−i2000000000000
χ522-2-22-2-22202020-20-20-222-20−222−2−222−2000000−2i2i00002−2−222i−2ii2−i2−i2i2i2−i2−i2i2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-4-4-44-44040-40-40000000000000004-4000000000000000000000000000000000000
χ55444-4-4-44-44040-40-4000000000000000-44000000000000000000000000000000000000
χ56444-4-4-44-4-40-40404000000000000000000000000000000000000000000000002i2−2i20000
χ57444-4-4-44-4-40-4040400000000000000000000000000000000000000000000000−2i22i20000
χ5844-444-4-4-440-40-40400000000000000000004-400000000000000000000000000000000
χ5944-444-4-4-440-40-4040000000000000000000-4400000000000000000000000000000000
χ6044-444-4-4-4-404040-4000000000000000000000000000000000000000000000000022−2200
χ6144-444-4-4-4-404040-40000000000000000000000000000000000000000000000000−222200
χ6244-4-4-44-44-4-444-4-444-4000040000000000000000000000000000000000000000000000
χ634-44-44-4-440-404040-40000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ644-44-44-4-440-404040-4000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ654-4-44-4-4440-40-4040400000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-44-4-4440-40-40404000000−222222−2222−22−222200000000000000000000000000000000000000
χ678-888-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).